Lesson 7 | Unit Rates and Percent | 6th Grade Mathematics

Objective

Solve measurement unit conversion problems.

Common Core Standards

Core Standards

The core standards covered in this lesson

6.RP.A.3.D — Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Ratios and Proportional Relationships

6.RP.A.3.D — Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Foundational Standards

The foundational standards covered in this lesson

4.MD.A.1

Measurement and Data

4.MD.A.1 — Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), …
4.MD.A.2

Measurement and Data

4.MD.A.2 — Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
5.MD.A.1

Measurement and Data

5.MD.A.1 — Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Identify information that is needed to solve a unit conversion problem.
Given one unit rate, determine a unit rate in the other direction.
Multiply or divide by the unit rate to solve unit conversion problems.
Compare and order measurements given in different units by converting them to the same unit.
Attend to the meaning of quantities and units to identify the need for unit conversion (MP.2).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Students should continue to use ratio and rate reasoning to determine their strategy to solve problems, and become more familiar with efficient methods involving multiplying or dividing by the unit rate.

Lesson Materials

Calculators (1 per student) — See note from lesson 1.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Malik is using a cookbook to make a recipe, but he cannot find his measuring cups! He has, however, found a tablespoon. Inside the back cover of the cookbook, it says that 1 cup = 16 tablespoons.

a. Explain how he could use the tablespoon to measure out the following ingredients:

2 cups of flour
$$\frac{1}{2}$$ cup sunflower seeds
$$1\frac{1}{4}$$ cup of oatmeal

b. Malik also adds the following ingredients. How many cups of each did he add?

28 tablespoons of sugar
6 tablespoons of cocoa powder

Guiding Questions

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References

Illustrative Mathematics Simple Unit Conversion Using Ratio Reasoning

Simple Unit Conversion Using Ratio Reasoning, accessed on July 25, 2017, 12:08 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

In Europe, the speed limits on the highways are posted in kilometers per hour. In the United States, the speed limits are posted in miles per hour. What is the equivalent rate of 65 miles per hour in kilometers per hour?

Guiding Questions

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Problem 3

Over the course of one day, you drank 3 quarts of water. Your sister drank 4 liters of water. Who drank more water? Show how you determine your answer.

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Three students created toy cars for a science project. The car that traveled the farthest distance when released down a ramp would win first prize. When the students each reported the distance their cars traveled, they realized that they all measured in different units. Help the students determine whose car won first place.

Car A	Car B	Car C
$$3 \frac{1}{2}$$ yards	13 feet	360 centimeters

Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Include problems similar to Anchor Problem #1, where students change recipes into differently measured units.
Include comparison and ordering problems where measurements are given in different units, within and between measurement systems.
Include problems where students are given a rate and asked for the rate in a different unit. For example, Blackberries cost $6 per pound; how much do they cost per ounce?

Open Up Resources Grade 6 Unit 3 Lesson 4
Illustrative Mathematics Converting Square Units
Illustrative Mathematics Currency Exchange

Lesson 6

Lesson 8

Lesson Map

Topic A: Defining Rate & Solving Rate Problems

Investigate and use rate in real-world situations.

6.RP.A.3 6.RP.A.3.B

Define rate and unit rate, and find rates from situations involving ratios.

6.RP.A.2 6.RP.A.3.B

Find unit rates and use them to solve problems.

6.RP.A.2 6.RP.A.3.B

Compare situations using unit rates, including speed, price, and work problems.

6.RP.A.3.B

Solve challenging problems involving unit rate.

6.RP.A.2 6.RP.A.3 6.RP.A.3.B

Topic B: Measurement Unit Conversions

Reason with measurement units and solve unit conversion problems using different strategies.

6.RP.A.3.D

Solve measurement unit conversion problems.

6.RP.A.3.D

Topic C: Percent

Define percent as a rate per 100. Find percentages of 100 and 1.

6.RP.A.3.C

Solve percent problems using benchmark fractions and percentages, with and without written work.

6.RP.A.3.C

Convert between fractions, percent, and decimals.

6.RP.A.3.C

Find a percent of a quantity.

6.RP.A.3.C

Find the whole quantity, given a part and percent.

6.RP.A.3.C

Solve percent problems, including finding percent when given a part and a whole.

6.RP.A.3.C

Solve multi-step problems involving rate and percent.

6.RP.A.2 6.RP.A.3 6.RP.A.3.C 6.RP.A.3.D

Unit Rates and Percent

Objective

Common Core Standards

Core Standards

Ratios and Proportional Relationships

Foundational Standards

Measurement and Data

Measurement and Data

Measurement and Data

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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